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Find the general solution to the equation sin(2x)-cos(2x)=0

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4 Answers

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Hint:

$\sin(\theta)=\cos(\theta)$ when $\theta=\dfrac{\pi}4+{n\pi}.$

Now solve $2x=\theta.$

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Hint: Use that $$\sin(x)-\cos(y)=-2 \sin \left(-\frac{x}{2}-\frac{y}{2}+\frac{\pi }{4}\right) \sin \left(-\frac{x}{2}+\frac{y}{2}+\frac{\pi }{4}\right)$$

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Hint: If $\sin(2x)=\cos(2x)$, then $\tan(2x)=1$.

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$$\sin2x=\cos2x$$

$$\tan2x=\dfrac{\sin2x}{\cos2x}=1=\tan\dfrac\pi4$$

Alternatively $$cos2x=\sin2x=\cos(\pi/2-2x)$$

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